Homework 6. Question Points Score Query Optimization 20 Functional Dependencies 20 Decompositions 30 Normal Forms 30 Total: 100

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1 Carnegie Mellon University Department of Computer Science /615- Database Applications C. Faloutsos & A. Pavlo, Spring 2015 Prepared by Vinay & Jiayu DUE DATE: Tuesday, 3/24/2015, 1:30pm Homework 6 IMPORTANT Deposit hard copy of your answers in class at 1:30pm on Tuesday, 3/24/2015. Separate answers, as usually, i.e., please solve each of the 4 questions on a separate page, and type the usual, full information, on each page: your name, Andrew ID, course #, Homework #, and Question #. Reminders Plagiarism: Homework may be discussed with other students, but all homework is to be completed individually. Typeset all of your answers whenever possible. Illegible handwriting may get no points, at the discretion of the graders. Late homeworks: please late homeworks to all TAs with the subject line exactly Homework Submission (HW 6) and the count of slip-days you are using. For your information: Graded out of 100 points; 4 questions total Rough time estimate: 6 hours (1-2 hours for each question) Revision : 2015/03/18 19:04 Question Points Score Query Optimization 20 Functional Dependencies 20 Decompositions 30 Normal Forms 30 Total: 100 1

2 15-415/615 Homework 6, Page 2 of 7 Tuesday, 3/24/2015, 1:30pm Question 1: Query Optimization [20 points] For this problem we consider a movie reviewing database with following three tables: 1. Movies(title, imdb number, year), where the primary key is imdb number; 2. Reviewers(userid, username), where the primary key is userid; 3. Reviews(userid, imdb number, rating, comment), where the primary key is (userid, imdb number), userid is foreign key referencing Reviewers, and imdb number is foreign key referencing Movies. For these tables we know the following statistics: Movies consists of N 1 = 60, 000 tuples, there are: 40,000 distinct movie titles, 90 distinct years, inclusive. Reviewers consists of N 2 = 50, 000 tuples, there are: 50,000 distinct userids, 50,000 distinct usernames Reviews consists of N 3 = 1, 300, 000 tuples, there are: 38,000 distinct userids, 33,000 distinct movie titles, 5 distinct ratings (i.e. 1, 2, 3, 4, and 5) without nulls. For the queries below, assume that there are no correlations between the columns of a table nor any prior knowledge about the data (i.e., assume uniform distribution). Estimate the number of resulting tuples for the query, and give the answer with fourth significant digit accuracy. We will accept either rounding half up or down, but no partial credit will be given. (a) [3 points] SELECT * FROM Movies WHERE year = 2001; (b) [4 points] SELECT * FROM Movies WHERE year = 1999 AND title = Fight Club (c) [4 points] SELECT * FROM Reviews WHERE rating > 3 (a) (b) (c) (d) [4 points] SELECT year, count(*) FROM Movies GROUP BY year (d) Question 1 continues...

3 15-415/615 Homework 6, Page 3 of 7 Tuesday, 3/24/2015, 1:30pm (e) [5 points] SELECT count(*) FROM Movies JOIN Reviews ON Movies.imdb number = Reviews.imdb number GROUP BY Movies.title (e) Homework 6 continues...

4 15-415/615 Homework 6, Page 4 of 7 Tuesday, 3/24/2015, 1:30pm Question 2: Functional Dependencies [20 points] 2.1 Consider the following legal instance of a relational schema S with attributes ABC: S A B C α 9 T α 16 F β 20 F Table 1: Legal instance of schema S for question 2.1 (a) Which of the following dependencies are violated by the instances of S in Table 1? i. [1 point] Yes No : A B is violated. ii. [1 point] Yes No : B A is violated. iii. [1 point] Yes No : C A is violated. iv. [1 point] Yes No : AC B is violated. v. [1 point] Yes No : B AC is violated. (b) [1 point] By only observing the instance of S in Table 1, can you identify the functional dependencies that hold on schema S? Yes No 2.2 For the next set of questions consider the relational schema r = {P, Q, R, S, T, U, V } and the set of functional dependencies FD: P Q (1) Q R (2) P S T RV (3) QT UR (4) S V (5) (a) [3 points] Which of the following is a minimum cover of the FD? (a) The given FD is a minimum cover. (b) {P Q, Q R, P S T, QT UR, S V } (c) {P Q, Q R, P T, Q U, S V } (d) {P Q, Q R, P S T, QT U, S V } (e) none of the above - the cover is (b) Yes/No: Which of the following functional dependencies can be deduced, from the above set of functional dependencies (Eq. (1)-(5))? Question 2 continues...

5 15-415/615 Homework 6, Page 5 of 7 Tuesday, 3/24/2015, 1:30pm i. [1 point] Yes No : P R ii. [2 points] Yes No : P S U iii. [2 points] Yes No : QS U iv. [2 points] Yes No : QST P (c) [2 points] True or False: The attribute closure {Q} + is {Q, R, T }. True False (d) [2 points] True or False: The attribute closure {P S} + is {P, Q, R, S, T, U, V }. True False Homework 6 continues...

6 15-415/615 Homework 6, Page 6 of 7 Tuesday, 3/24/2015, 1:30pm Question 3: Decompositions [30 points] 3.1 For this set of questions, Consider the relation with attributes, S = {A, B, C, D, E, F }, Let the following functional dependencies F D be defined over the relation S: A D A E D C D F (a) [6 points] Provide the attribute closure of {AB}. (b) Identify whether the decomposition ABC, CDE, EF A is lossless and dependencypreserving? (c) Identify whether the decomposition ABCE, ADC, ADEF is lossless and dependency-preserving? 3.2 Consider the relation with attributes, A = {P, Q, R, S, T, U, V }. The following functional dependencies hold over A. RT P QS T R Q (a) Identify whether the decomposition QST, QR, P RSU V is lossless and dependencypreserving? (b) Identify whether the decomposition QST, QR, P RSUV, P RT is lossless and dependency-preserving? Homework 6 continues...

7 15-415/615 Homework 6, Page 7 of 7 Tuesday, 3/24/2015, 1:30pm Question 4: Normal Forms [30 points] Consider the relation with attributes, S = {A, B, C, D, E}. Let the following functional dependencies be defined over the relation S, A BC CD E B D E A (a) Identify whether this relationship in 3NF and/or BCNF? i. [2 points] Yes No : 3NF ii. [2 points] Yes No : BCNF (b) [5 points] Provide the projection of FDs for the subset of attributes {ABD} (c) [8 points] Give a BCNF decomposition of S that is lossless. (d) [3 points] Is your BCNF decomposition dependency preserving? True False Give a 3NF decomposition of S that is lossless and dependency pre- (e) [10 points] serving. End of Homework 6

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